math
On beauty bare
Wang tiles
Trees and graphs
A tree is a kind of graph, but a graph can be considerably more complex than a tree.
I have reason to believe, which for brevity’s sake I will treat elsewhere, that the most complex class of processes and structures we humans can consciously prescribe, reduces mathematically to a tree. A tree has a top, bottom, left and right. Its branches fan out from the trunk and they don’t intersect with one another. They are discrete, contiguous, identifiable objects which persist across time. Trees are Things.
Software and websites, however, reduce to arbitrarily more complex structures: they are graphs. A graph has no meaningful orientation whatsoever. No sequence, no obvious start or end—at least none that we can intuit. It is better considered not as one Thing, but as a federation of Things, like the brain or a fungus network, or perhaps a composite artifact left behind from an ongoing process, like an ant colony or human city.
Trees and semilattices
The tree of my title is not a green tree with leaves. It is the name of an abstract structure. I shall contrast it with another, more complex abstract structure called a semilattice.
Both the tree and semilattice are ways of thinking about how a large collection of many small systems goes to make up a large and complex system.
A collection of sets forms a semilattice if, and only if, when two overlapping sets belong to the collection, the set of elements common to both also belongs to the collection. That is, if [234] and [345] belong to the collection, then [34] belongs to the collection.
A collection of sets forms a tree if, and only if, for any two sets that belong to the collection either one is wholly contained in the other, or they are wholly disjoint. Every tree is trivially a simple semilattice.
We are concerned with the difference between structures in which no overlap occurs, and those structures in which overlap does occur.
The semilattice is potentially a much more complex and subtle structure than a tree. It is this lack of structural complexity, characteristic of trees, which is crippling our conceptions of the city.
A City Is Not a Tree
An Essay by Christopher Alexander- Strands of life
- Impending destruction
- The right overlap
- The difficulty of designing complexity
- Political chains of influence
Notes on the Synthesis of Form
A Book by Christopher AlexanderVisualizing Data
A Book by William S. ClevelandExploratory Data Analysis
A Book by John TukeyPlus Equals #4
An Article by Rob WeychertOne of the seeds for Plus Equals was planted a few years ago with Incomplete Open Cubes Revisited, my extension of a Sol LeWitt work. I learned a lot about isometric projection from that project, but my affection for the concept didn’t begin there. Whether I’m looking at a Chris Ware illustration or an exploded-view technical drawing of a complex machine, an isometric rendering always stirs something in me.
A brief foray into vectorial semantics
An Article by James SomersOne of the best (and easiest) ways to start making sense of a document is to highlight its “important” words, or the words that appear within that document more often than chance would predict. That’s the idea behind Amazon.com’s “Statistically Improbable Phrases”:
Amazon.com’s Statistically Improbable Phrases, or “SIPs”, are the most distinctive phrases in the text of books in the Search Inside!™ program. To identify SIPs, our computers scan the text of all books in the Search Inside! program. If they find a phrase that occurs a large number of times in a particular book relative to all Search Inside! books, that phrase is a SIP in that book.
tixy.land
A Websitesin(t * x) * cos(t * y)
Creative code golfing.
Rafael Araujo's Golden Ratio
A GalleryBlue Morpho Double Helix & Icosahedron
The Tiling Patterns of Sebastien Truchet and the Topology of Structural Hierarchy
A Research Paper by Cyril Stanley SmithA pattern of tiles illustrated by Douat in 1722.
A translation is given of Truchet's 1704 paper showing that an infinity of patterns can be generated by the assembly of a single half—colored tile in various orientations.
Everything and More
A Book by David Foster WallaceInfoCrystal
A Research PaperThis paper introduces a novel representation, called the InfoCrystal, that can be used as a visualization tool as well as a visual query language to help users search for information. The InfoCrystal visualizes all the possible relationships among N concepts.
Open Transclude for Networked Writing
Not an accumulation of facts
Knowledge is not an accumulation of facts, nor is it even a set of facts and their relations. Facts are only rendered meaningful within narratives, and the single-page document is a format very conducive to narrative structure. The hypertext books that have gained popularity (I’m thinking here of Meaningness.com) have largely conformed to this in two ways: 1) there is an intended reading order, and 2) the longer essays within the project do most of the heavy lifting in terms of imparting the author’s perspective to readers.
On the other hand, the notion of the “document” that is intrinsic to web development today is overdetermined by the legacy of print media. The web document is a static, finished artifact that does not bring in dynamic data. This is strange because it lives on a medium that is alive, networked, and dynamic, a medium which we increasingly understand more as a space than a thing.
More that can be done
The web is still a very young medium, and it has been influenced more than anything else by print media design. There is so much more that can be done with text on a screen than is being done today. Citations, drawing, chat, speech-to-text. There are opportunities everywhere, and the bar is low! If we are serious about unlocking the value of knowledge we should consider how to improve every part of the knowledge production stack, and that includes reading. As Laurel Schwulst says:
Imaginative functionality is important, even if it’s only a trace of what was, as it’s still a sketch for a more ideal world.
Open Transclude
What you are looking at is an scroll-locked iframe that links to a quote I picked out of my blog post “Notes on Comparative Psychology.” You can use Open Transclude anywhere you can drop an
<a>
tag on your own site.Open Transclude:
- Works anywhere on your own domain
- Compatible with most static site generators / templating engines
- 12 lines of HTML, 80 lines of SCSS, 22 lines of JS (4.5 kb total)
- Has 0 dependencies — this is native web technology
Open Transclude is extremely simple, and the heaviest part of the code is the CSS, which you can simplify at your whim. That’s why I am referring to it as a UX pattern. This is not a protocol. The code is really a commodity. What’s interesting about it is the idea and the design, and this is just one viable implementation! Feel free to adapt it however you like.
The principal improvement over a block quotation is sense of context.